In late July, Joe Daniels, the president of the National September 11 Memorial & Museum foundation, addressed a reception in a garden at the residence of the U.S. deputy chief of mission in Tokyo. In attendance were family members of Japanese citizens killed in the attacks, Japanese firefighters who had flown to New York to help in the recovery effort and corporate executives invited to learn more about the memorial and the museum scheduled to open next spring.

As guests nibbled on sushi, chicken and pasta, Mr. Daniels held off on asking for donations. But the event was part of an expanding effort to raise money overseas to fund the organization's projected $60 million operating budget.

To date, the foundation says it has raised about $15 million from foreign donors. Foundation officials have made trips to France, England and Ireland, and are planning a trip to Germany in the coming year.

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As the 9/11 Memorial Museum's opening nears, questions remain about how the foundation will operate both the museum and the memorial plaza without help from Congress. The memorial in 2011 asked for $20 million in annual federal funding in a bill sponsored by the late Sen. Daniel Inouye of Hawaii. That effort stalled, and foundation officials and the New York congressional delegation haven't yet formed a plan to reintroduce the bill or craft a new one.

Mr. Daniels said the foundation needs federal assistance, but "until that day comes, our biggest responsibility to the public is to keep the museum open."

He said he hopes the foundation can cover 60% of its operating budget with earned revenue, including admissions, gift-shop sales and concessions, leaving a gap of $24 million to be filled by private donations. The museum plans to charge roughly $20 for adult admission—a move that has prompted some criticism. Victims' family members will be admitted for free, and the museum will be free to the public for several hours each week.

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Steel tridents recovered from the World Trade Center site will be seen in the entry pavilion of the museum.
Kevin Hagen for The Wall Street Journal

By contrast, the United States Holocaust Memorial Museum, which doesn't charge admission, received $48.1 million in federal funds for the 2013 fiscal year, covering 60% of its $80.7 million budget.

Meanwhile, the Oklahoma City National Memorial & Museum raises about $1.5 million a year to support its $3.3 million operating budget, said Executive Director Kari Watkins. It doesn't receive federal assistance.

The 9/11 Memorial plaza welcomed 5 million visitors last year. The foundation projects that 2.5 million people will attend the museum each year.

The museum is now in the final stages of construction, after a series of delays and disputes over construction costs with the Port Authority of New York and New Jersey, which owns the site. The foundation, chaired by Mayor Michael Bloomberg, estimates the cost of construction for both the memorial and the museum at $700 million.

Foundation officials are counting on the fact that the Sept. 11, 2001, terrorist attacks were a global event, watched in real-time by people around the world. Some 90 countries lost citizens in the attacks, and visitors to the memorial have come from nearly 200 countries.

Foundation officials said they are hoping to replicate a strategy they have used successfully in France, where they found an early ally in former U.S. Ambassador Craig Stapleton.

Mr. Stapleton, who served as ambassador to France from 2005 to 2009, held a reception in his residence in Paris in 2008 for the 9/11 Memorial foundation. One of the speakers was Christy Ferer, who lost her husband, Neil Levin, on Sept. 11 and now serves on the foundation board as co-chairwoman of its development committee.

"We feel what happened on Sept. 11 belongs to the world," she said in an interview. "The pain knew no boundaries."

And on a practical level, she said, the memorial offers an opportunity for international firms that do business in the U.S. to show their support for America.

When Mr. Stapleton returned to the U.S. in 2009, he joined the 9/11 Memorial foundation's board, and made subsequent trips to France to meet with prospective donors, several of whom had supported the commission of a sculpture in the garden of the ambassador's residence in Paris. Mr. Stapleton said he scored an 80% success rate in those meetings, garnering about $2 million in donations for the memorial.

One of those donors was Léone-Noëlle Meyer, a pediatrician and adopted granddaughter of the founder of the French department-store company Galeries Lafayette.

Dr. Meyer, who is Jewish, said she was the only member of her biological family to survive the Holocaust, and she still feels gratitude to the U.S. for helping defeat the Nazis in World War II.

"I was struck by the way that Sept. 11 happened, the way that all these people died," said Dr. Meyer, who is president of Phison Capital, a family-owned finance and investment company.

She donated between $250,000 and $499,999, according to a list of donations provided by the foundation. "It was a gesture, a little solidarity—we don't forget you," she said.

To date, Mr. Daniels said the foundation has raised $455 million in private donations. Tax-funded grants have covered $390 million in construction costs.

The foundation's $15 million tally includes $5 million from Barclays—the result of outreach in London—and $5 million from Sharp Electronics Corp., the U.S. arm of Osaka-based Sharp Corp.SHCAY0.00%, in a gift that originated in the U.S.

Other international gifts include $500,000 from the Royal Bank of Canada, $250,000 from Zurich-based Swiss Re and $100,000 from the Qatar Museums Authority.

"We share in the sense of grief felt by the people of New York and all those who lost friends and loved ones in the tragedy of 9/11," said Federica Zuccarini, a spokeswoman for the authority, which is a government institution run by the ruling Al Thani family.

Ms. Ferer said Mr. Bloomberg's involvement has helped seal the deal with some international donors.

She said she has taken visiting foreign executives, including Christophe de Margerie, chairman and chief executive of French oil company Total SA, to meet Mr. Bloomberg for coffee in the bullpen at City Hall before a tour of the World Trade Center site.

Total USA subsequently made a gift of between $100,000 and $249,000.

Last February, Ms. Ferer introduced Mr. Bloomberg to a group of visiting Chinese investors in a gathering at the Empire State Building. She hasn't invited them to make donations yet, but she said she plans to invite them back, and this time take them on a tour of the memorial.

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